A flight plan is the detailed description of the route to be followed by an aircraft within the framework of a planned flight. The flight plan is usually managed aboard civil aeroplanes by a system referred to as a “Flight Management System”, which will be called FMS hereinafter, which places the route to be followed at the disposal of the flight personnel and at the disposal of the other on-board systems. Among other things, these systems allow navigation assistance, by displaying information which is useful to pilots, or else by communicating flight parameters to an automatic piloting system.
FIG. 1 presents an overview illustrating the structure of an FMS known from the prior art. A system of FMS type 10 has a man-machine interface 12 comprising for example a keyboard and a display screen, or else simply a display touchscreen, as well as at least the following functions, described in ARINC standard 702:                Navigation (LOCNAV) 101, for performing optimal location of the aircraft as a function of geo-location means 130 such as satellite based geo-positioning or GPS, GALILEO, VHF radionavigation beacons, inertial platforms. This module communicates with the aforementioned geo-location devices;        Flight plan (FPLN) 102, for inputting the geographical elements constituting the skeleton of the route to be followed, such as points imposed by the departure and arrival procedures, waypoints, airways;        Navigation database (NAVDB) 103, for constructing geographical routes and procedures on the basis of data included in the bases relating to the points, beacons, interception legs or altitude legs . . . ;        Performance database, (PRFDB) 104, containing the craft's aerodynamic and engine parameters;        Lateral trajectory (TRAJ) 105, for constructing a continuous trajectory on the basis of the points of the flight plan, complying with the performance of the aircraft and the confinement constraints (RNP); the functions forming the subject of the present invention affect inter alia this part of the calculator.        Predictions (PRED) 106, for constructing an optimized vertical profile on the lateral trajectory.        Guidance (GU ID) 107, for guiding the aircraft in the lateral and vertical planes on its three-dimensional trajectory, while optimizing its speed. In an aircraft equipped with an automatic piloting device 11, the latter can exchange information with the guidance module 107;        Digital data link (DATALINK) 108 for communicating with the control centres and other aircraft 13.        
The flight plan is entered by the pilot, or else by data link, on the basis of data contained in the navigation database. A flight plan is devised on the basis of a list of waypoints and of procedures (departure, arrival, airways, missions) stored in the navigation database 130.
The pilot thereafter inputs the aircraft parameters: mass, flight plan, span of cruising levels, as well as one or a plurality of optimization criteria, such as the CI.
The flight plan comprises an ordered series of segments (usually called LEGs) defined by an aeronautical standard. A segment corresponds to a directive for calculating an elementary trajectory. The trajectory arising from the flight plan PV is constructed gradually from segment to segment on the basis of the directives contained in each segment (inter-waypoint geometry defined by these segments), of the performance of the aeroplane, of constraints of any type (altitude, speed, time, slope) and of the thrust and speed directives (which are used for the calculation of the turning radius). In commercial aeronautics the ARINC 424 international standard defines various types of “LEG” or segment, each type corresponding to a kind of data required for the calculation of the elementary trajectory corresponding to the type, for example directives to be followed in terms of position, altitude, heading or route.
More specifically, the modules TRAJ 105 and PRED 106 calculate respectively the lateral trajectory and the vertical profile, that is to say the flight profile in terms of altitude and speed, which for example minimizes the optimization criterion.
Each segment thus generates a portion of trajectory or elementary trajectory. This elementary trajectory corresponds to a geometric element which can be a straight section, an arc, typically a circular arc, or combinations of straight section and arcs.
Furthermore a trajectory portion making it possible to link the elementary trajectories corresponding to two nonaligned consecutive segments is termed a transition T. The existence of a transition between two segments therefore necessarily gives rise to a turning of the aircraft during the transition.
On the basis of the complete calculation of the trajectory, the FMS determines “predictions” (carried out by the module PRED) which correspond to values of key parameters of the trajectory along the latter, that is to say for various values of the curvilinear abscissa x of the trajectory. Typically these parameters are: speed of the aircraft relative to the surrounding air mass termed CAS (for Calibrated Air Speed), Altitude of the aircraft, Wind (defined by vector).
The FMS can, on instruction from the pilot, slave the aircraft automatically to the calculated trajectory.
A transition is characterized by a transition start point, which may be a point calculated by the FMS or the real-time position of the aircraft, and an end-of-transition item of information, which may be a point, a heading, or a combination of a point which must be overflown according to a certain heading. According to the prior art the curved part of the transition takes the form of one or more circular arcs of amplitude lying between 2 and 358 degrees and of single and constant radius R0.
Generally the turning radius R is dependent on a set of parameters such as: speed of the aircraft relative to the surrounding air mass (termed CAS for “Calibrated Air Speed”); the wind W (in the form of a vector); the altitude; the temperature outside the aircraft.
For example, the formula is known:R=GS2/g·tan(φN)  (1)    With:    GS ground speed of the aircraft,    g gravitational constant    φN nominal roll angle predetermined as a function of the performance and of the type of aircraft.    We have the following vector equality:GS=TAS+W  (2)    With TAS “True Air Speed”, corresponding to the CAS speed corrected for the altitude of the aircraft and for the exterior temperature around the aircraft.
The FMS calculates, for a given transition, a single radius R0 on the basis of a single set of values of parameters. The fixed value of each parameter is defined as a function of the transition: average value, “worst case” (for example for the wind, see hereinbelow), value at the transition start point (example: altitude and temperature) etc. The single turning radius R0 is termed “conservative” in the sense that it is calculated in such a way that the trajectory is flyable whatever hazards are encountered along the trajectory.
A first example is illustrated in FIG. 2, for a calculation of transition T between a transition start point WPA and a transition end point WPB comprising a circular arc T0 between WPA and the point I and a straight part between I and WPB. Here the aircraft is slaved to the calculated trajectory which is frozen.
W0 represents the wind vector at the point WPA. The effect of the wind is obtained by projecting the wind vector onto the lateral trajectory. The worst case of impact of the wind on the aeroplane corresponds to the case for which the aircraft has the largest ground speed GS, i.e. a wind vector substantially collinear with the air speed of the aircraft. According to the prior art the wind effect taken into account by the FMS for the calculation of the turning radius R0 is the “worst case” for a wind W0 (that is to say considered at the start of the transition) extrapolated over the whole of T0. However, the value of the parameters can vary greatly along a transition, rendering the set of values of the parameters used for the calculations less representative. In the example the worst case of wind occurs only at the end of T0, on the portion T3. Thus R0 is calculated with the highest speed of the aircraft GSmax attained by the aircraft at the end of the transition.
The aircraft slaved to the conservative trajectory T, calculated by the FMS and frozen, therefore flies a large part of T0 at a smaller roll angle than the nominal roll and with a lower ground speed than GSmax. This low ground speed would have allowed the aircraft to fly at the nominal roll according to a smaller turning radius (see formula (1)). In fact over the whole start of T0, having regard to the direction of the wind W0 relative to the start of the trajectory, the aircraft would have been able to fly a “tighter” trajectory the commencement of which is illustrated by TF1 or TF2 in FIG. 2, corresponding to a turning radius which is smaller than R0. The conservative trajectory T0 is therefore non-optimized with respect to the flyable trajectory, and of larger area on the horizontal plane.
FIG. 3 illustrates a second example, for the case of a calculation of transition between a transition start point PA corresponding to the position of the aircraft A and a heading HD. According to the prior art, when the aircraft flies a transition towards a heading, the trajectory is not frozen as previously and it is the trajectory calculation which is refreshed automatically as the aircraft progresses. In this example it is also considered that the worst case of ground speed occurs only at the end of the transition.
The FMS begins by calculating a first conservative trajectory TCO of radius R0 (“worst case”). When the conditions (values of parameters, typically the ground speed) at the start of transition are more favourable than those that served for the conservative calculation, the aircraft, which here is not slaved to the trajectory calculated as in the previous example, will in reality fly a tighter trajectory TF0. Indeed, the aircraft flying at nominal roll angle φN, the trajectory radius actually flown by the aircraft is determined by the value of the ground speed GS (see formula (1)). If the latter is lower than expected, the turning radius actually flown is smaller than R0.
Here the FMS recalculates and refreshes the trajectory automatically. The automatic refreshing is triggered either at regular intervals, or for example when the FMS detects that the real position of the aircraft differs by a certain disparity from the calculated position, such as illustrated at the point Refresh #1. The FMS then recalculates a first trajectory TC1, but still on the basis of the “worst case” which will occur only at the end of the transition, that is to say with a radius still equal to R0. But instead of flying TC1, the aircraft for the same reasons as previously flies a tighter trajectory TF1. When the real position again differs substantially from the calculated position, at Refresh2# for example, the FMS recalculates TC2, still with the “worst case” (radius R0) but flies TF2.
Finally at Refresh3# the FMS recalculates TC3 (still of radius R0) which this time will actually be flown by the aircraft on account of the fit between the value of the real ground speed and the value of the ground speed taken for the calculation of R0.
Thus during the flight by the aeroplane of the transition, new trajectories are recalculated at each refresh and displayed on the screens of the aeroplane cockpit. A consequence is that these calculated trajectories are not representative of the trajectory actually flown, and that the trajectory calculated and displayed by the FMS is not stable.
Moreover in this case, the predictions carried out at the start of transition on the basis of TC0 are erroneous, and the pilot will see the predictions evolve in tandem with the refreshes. This instability of the predictions affects the crew's ability to adhere to an RTA (Requested Time to Arrival).
This type of problem arises, for example, in the case of strong wind (and will be accentuated by a large transition angle), and on the other hand in the case of a large variation in speed along the transition (and it will be accentuated by a long transition).
Moreover, the technical problems described hereinabove and associated with the current mode of calculation of the transitions from a point (calculated point or real-time position of the aircraft) towards a point or a heading can in certain cases reduce the flight possibilities of departure and/or arrival procedures of airports situated in dangerous zones (such as mountainous zones) although aeroplane performance permits same.
An aim of the present invention is to alleviate the aforementioned drawbacks by proposing a method for calculating a trajectory intended to be flown by an aircraft exhibiting improved, flyable, reliable transitions that are tailored to the performance of the aircraft.